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- Multiplicative_inverse abstract "In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).The term reciprocal was in common use at least as far back as the third edition of Encyclopædia Britannica (1797) to describe two numbers whose product is 1; geometrical quantities in inverse proportion are described as reciprocall in a 1570 translation of Euclid's Elements.In the phrase multiplicative inverse, the qualifier multiplicative is often omitted and then tacitly understood (in contrast to the additive inverse). Multiplicative inverses can be defined over many mathematical domains as well as numbers. In these cases it can happen that ab ≠ ba; then \"inverse\" typically implies that an element is both a left and right inverse.The notation f −1 is sometimes also used for the inverse function of the function f, which is not in general equal to the multiplicative inverse. For example, the multiplicative inverse 1/(sin x) = (sin x)−1 is the cosecant of x, and not the inverse sine of x denoted by sin−1 x or arcsin x. Only for linear maps are they strongly related (see below). The terminology difference reciprocal versus inverse is not sufficient to make this distinction, since many authors prefer the opposite naming convention, probably for historical reasons (for example in French, the inverse function is preferably called application réciproque).".
- Multiplicative_inverse thumbnail Hyperbola_one_over_x.svg?width=300.
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- Multiplicative_inverse wikiPageWikiLink Algorithm.
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- Multiplicative_inverse wikiPageWikiLink Category:Abstract_algebra.
- Multiplicative_inverse wikiPageWikiLink Category:Elementary_algebra.
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- Multiplicative_inverse wikiPageWikiLink Category:Multiplication.
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- Multiplicative_inverse wikiPageWikiLink Invertible_matrix.
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- Multiplicative_inverse wikiPageWikiLink File:Hyperbola_one_over_x.svg.
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- Multiplicative_inverse wikiPageWikiLinkText "''1/x''".
- Multiplicative_inverse wikiPageWikiLinkText "Inverse".
- Multiplicative_inverse wikiPageWikiLinkText "Multiplicative inverse Algorithms".
- Multiplicative_inverse wikiPageWikiLinkText "Multiplicative inverse".
- Multiplicative_inverse wikiPageWikiLinkText "Reciprocal".
- Multiplicative_inverse wikiPageWikiLinkText "algorithm to generate reciprocals".
- Multiplicative_inverse wikiPageWikiLinkText "inverse".
- Multiplicative_inverse wikiPageWikiLinkText "inversion mapping".
- Multiplicative_inverse wikiPageWikiLinkText "inversion".
- Multiplicative_inverse wikiPageWikiLinkText "inverted".
- Multiplicative_inverse wikiPageWikiLinkText "multiplicative inverse algorithm".
- Multiplicative_inverse wikiPageWikiLinkText "multiplicative inverse".
- Multiplicative_inverse wikiPageWikiLinkText "multiplicative inversion".
- Multiplicative_inverse wikiPageWikiLinkText "reciprocal function".
- Multiplicative_inverse wikiPageWikiLinkText "reciprocal".
- Multiplicative_inverse wikiPageWikiLinkText "reciprocals".
- Multiplicative_inverse wikiPageWikiLinkText "reciprocation".
- Multiplicative_inverse wikiPageWikiLinkText "−1".
- Multiplicative_inverse wikiPageUsesTemplate Template:Math.
- Multiplicative_inverse subject Category:Abstract_algebra.